a) To find the electric field intensity between the plates, we can use the formula:
Electric field intensity = potential difference / distance between plates
In this case, the potential difference is 420 V and the distance between the plates is 0.1 m (10 cm converted to meters).
Electric field intensity = 420V / 0.1m = 4200 N/C
b) To find the tension in the thread, we can use the formula:
Tension = weight of the ball + force of the electric field
The weight of the ball can be found using the formula:
Weight = mass x acceleration due to gravity
In this case, the mass of the ball is 3.0 x 10^4 kg and the acceleration due to gravity is 9.8 m/s^2.
Weight = 3.0 x 10^4 kg x 9.8 m/s^2 = 2.94 x 10^5 N
The force of the electric field can be found using the formula:
Force = electric field intensity x charge
The charge on the ball is not given, so we cannot find the force.
c) The magnitude of the electric force deflecting the ball can be found using the formula:
Force = Electric field intensity x Charge
As the Charge on the ball is not given it's impossible to calculate this value
d) The Charge on the ball is not provided in the problem statement and it's impossible to calculate it without additional information
It's worth noting that this scenario is a thought experiment, and that the presence of a thread would alter the scenario, as well as the fact that the charge is not provided.